Subdividing a domain into a finite number of elements is desirable in numerous technical fields. For example, it is desirable to decompose a domain into a finite number of elements in connection with performing uncertainty quantification (UQ) and global optimization in applications such as multiscale material modeling and aerodynamic analysis. Robustness of conventional processes for performing domain decomposition is not trivial. Generally, domain decomposition breaks down a domain into a finite number of cells with certain desired properties, such as positive Jacobian, convex elements, and planar facets. A domain decomposition also defines how a point in the domain is assigned to a cell, and how each cell in the domain decomposition identifies cells in close proximity thereto.
Several different approaches have been proposed for performing domain decomposition over enclosed domains. These approaches, however, are associated with numerous deficiencies. In particular, conventional Voronoi domain decomposition (VDD) approaches rely on techniques such as successive hyperplane trimming in order to construct Voronoi cells. These techniques generally suffer from a curse of dimensionality, where as a number of dimensions of the domain increases, the computations required to construct the Voronoi cells increase exponentially.